In short, yes you can. But the means to do so depend on the type of notification channel you are working with.
With the Kahuna Marketing Friendly InApp messaging and Custom InApp messaging, you can specify how many days you would like the message to be valid during the campaign creation. If the end user does not return to the app within the number of days specified, the user will not see the InApp notification. The number of "expired" notifications will be reported within the campaign details page.
For push messages, Kahuna recently introduced a "TTL" (Time To Live) feature. How this works is that it leverages both Apple and Android's push message expiration feature. But it is important to point out that this will not remove the notification from a users connected phone once the expiration time has passed. What it means is that if the end user's phone has been turned off, is in Airplane Mode, or simply has had no cellular or wifi connection, and the expiration time has passed, the notification will not be delivered. To use this new TTL feature, you must use the Kahuna Push API (https://app.usekahuna.com/tap/public_docs/Content/APIs/Push.htm), and specify the TTL in seconds within the Push Payload. Currently there is no way to specify this expiration time in the Campaign Creation UI. The next iteration of the TTL feature will allow you to specify an expiration date instead of an amount of seconds, as well as bringing it out of the API and allowing you to specify this during Campaign Creation.